Most often, it's the Federal Marshalls that come a'knockin'.
Someone calls in with a "good faith" complaint (they try to qualify it for validity), they will attempt to get a sworn affadavit from the individual ("reasonable suspicion" must still be proven).
Court action is initiated, a search warrant is issued, and the marshalls hit the road heading your way. Because it is usually an inter-state commerce thing, the suit is usually Federal (hence, the Marshalls).
For the couple instances that I've heard about, the Marshals come in and order everyone out of the building or into a benign area (remain on the premises) ... the object is to remove the possibility of someone changing / removing / dumping the illegal materials.
The marshalls will audit / oversee the audit of all of the software on every machine. When the audit is complete, a demand will be made for the licenses of each software product. If the license count and product count don't agree, then action is decided and taken.
Easy enough.
Depending on other news of the day, you might even get a spot on the local news "Local company raided by FEDs due to possible software violations" ... great publicity. Certainly worth the couple hundred / thousands of dollars saved by bootlegging the software. The BSA might even call the news guys for you, it helps their cause to get the word out.
When I was working with a VAR, we had a couple customers with store rooms that held nothing but software licenses (this was before "Site Licenses" were popular and available) just to cover their legal a$$ for software usage.
FWIW
Scott